Unified analysis of kinematic and inertial earthquake pile responses via the single-input response spectrum method

• Kinematic pile response is important in a soft ground together with the inertial one.
• A complex-mode response spectrum method is appropriate in the pile–soil model.
• The kinematic, inertial and total responses can be evaluated in a unified manner.
• The superposition rule depends on the natural period of ground and structure.

In the seismic response of a structure–pile–soil system, a kinematic response due to the forced displacement of the surface ground is important, especially in a soft ground, together with the inertial response due to the inertial forces from superstructures. In this paper it is shown that a response spectrum method in terms of complex modal quantities can be used in the evaluation of the maximum kinematic and inertial seismic responses of the structure–pile–soil system to the ground motion defined at the engineering bedrock surface as an acceleration response spectrum. The notable point is that the kinematic response, the inertial response and the total response can be evaluated by the same analysis model and method by changing the model parameters. Then it is discussed which of the simple sum or the SRSS of the kinematic and inertial responses is appropriate even in resonant cases for the evaluation of the maximum pile-head bending moment. It is concluded through many examples that the validity of the simple sum or the SRSS depends on the relation between the fundamental natural period of the surface ground and that of the superstructure while an averaged evaluation is valid in resonant cases.